4.1 
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


4.1A 
Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard

Apply
MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE
Including, but not limited to:
 Mathematical problem situations within and between disciplines
 Everyday life
 Society
 Workplace
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.1. Interpret results of the mathematical problem in terms of the original realworld situation.
 IX.A. Connections – Connections among the strands of mathematics
 IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
 IX.A.2. Connect mathematics to the study of other disciplines.
 IX.B. Connections – Connections of mathematics to nature, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.
 IX.B.2. Understand and use appropriate mathematical models in the natural, physical, and social sciences.
 IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.

4.1B 
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
Process Standard

Use
A PROBLEMSOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEMSOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION
Including, but not limited to:
 Problemsolving model
 Analyze given information
 Formulate a plan or strategy
 Determine a solution
 Justify the solution
 Evaluate the problemsolving process and the reasonableness of the solution
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:
 I.B. Numeric Reasoning – Number sense and number concepts
 I.B.1. Use estimation to check for errors and reasonableness of solutions.
 V.A. Statistical Reasoning – Design a study
 V.A.1. Formulate a statistical question, plan an investigation, and collect data.
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.1. Analyze given information.
 VII.A.2. Formulate a plan or strategy.
 VII.A.3. Determine a solution.
 VII.A.4. Justify the solution.
 VII.A.5. Evaluate the problemsolving process.
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.2. Evaluate the problemsolving process.

4.1C 
Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
Process Standard

Select
TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, ESTIMATION, AND NUMBER SENSE AS APPROPRIATE, TO SOLVE PROBLEMS
Including, but not limited to:
 Appropriate selection of tool(s) and techniques to apply in order to solve problems
 Tools
 Real objects
 Manipulatives
 Paper and pencil
 Technology
 Techniques
 Mental math
 Estimation
 Number sense
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:
 I.B. Numeric Reasoning – Number sense and number concepts
 I.B.1. Use estimation to check for errors and reasonableness of solutions.
 V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
 V.C.2. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.

4.1D 
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard

Communicate
MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, AND LANGUAGE AS APPROPRIATE
Including, but not limited to:
 Mathematical ideas, reasoning, and their implications
 Multiple representations, as appropriate
 Symbols
 Diagrams
 Language
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:
 II.D. Algebraic Reasoning – Representing relationships
 II.D.1. Interpret multiple representations of equations, inequalities, and relationships.
 II.D.2. Convert among multiple representations of equations, inequalities, and relationships.
 VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
 VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
 VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
 VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
 VIII.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
 VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
 VIII.C. Communication and Representation – Presentation and representation of mathematical work
 VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
 VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
 VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
 IX.B. Connections – Connections of mathematics to nature, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.

4.1E 
Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard

Create, Use
REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
 Representations of mathematical ideas
 Organize
 Record
 Communicate
 Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
 Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:
 VIII.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
 VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
 VIII.C. Communication and Representation – Presentation and representation of mathematical work
 VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
 VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.

4.1F 
Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard

Analyze
MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
 Mathematical relationships
 Connect and communicate mathematical ideas
 Conjectures and generalizations from sets of examples and nonexamples, patterns, etc.
 Current knowledge to new learning
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.1. Analyze given information.
 VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
 VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
 VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
 VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
 VIII.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
 VIII.C. Communication and Representation – Presentation and representation of mathematical work
 VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
 VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
 VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
 IX.A. Connections – Connections among the strands of mathematics
 IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
 IX.A.2. Connect mathematics to the study of other disciplines.

4.1G 
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard

Display, Explain, Justify
MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION
Including, but not limited to:
 Mathematical ideas and arguments
 Validation of conclusions
 Displays to make work visible to others
 Diagrams, visual aids, written work, etc.
 Explanations and justifications
 Precise mathematical language in written or oral communication
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 Measuring angles
 Understanding decimals and addition and subtraction of decimals
 Building foundations for addition and subtraction of fractions
 TxCCRS:
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.4. Justify the solution.
 VII.B. Problem Solving and Reasoning – Proportional reasoning
 VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
 VII.C. Problem Solving and Reasoning – Logical reasoning
 VII.C.1. Develop and evaluate convincing arguments.
 VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
 VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
 VIII.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
 VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
 VIII.C. Communication and Representation – Presentation and representation of mathematical work
 VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.

4.5 
Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to:


4.5C 
Use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l x w).

Use
MODELS TO DETERMINE THE FORMULAS FOR THE PERIMETER OF A RECTANGLE (l + w + l + w OR 2l + 2w), INCLUDING THE SPECIAL FORM FOR PERIMETER OF A SQUARE (4s) AND THE AREA OF A RECTANGLE (l x w)
Including, but not limited to:
 Rectangle
 4 sides
 4 vertices
 Opposite sides congruent
 2 pairs of parallel sides
 4 pairs of perpendicular sides
 4 right angles
 Square (a special type of rectangle)
 4 sides
 4 vertices
 All sides congruent
 2 pairs of parallel sides
 4 pairs of perpendicular sides
 4 right angles
 Perimeter – a linear measurement of the distance around the outer edge of a figure
 Perimeter is an additive onedimensional linear measure
 Models to determine formulas for perimeter
 Rectangle (P = l + w + l + w or P = 2l + 2w)
 Square (P = 4s)
 Area – the measurement attribute that describes the number of square units a figure or region covers
 Area is a multiplicative twodimensional square unit measure.
 Models to determine formulas for area
 Rectangle (A = l × w)
 Square (A = s × s)
Note(s):
 Grade Level(s):
 Grade 4 introduces use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l × w).
 Grade 5 will use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l × w × h, V = s × s × s, and V = Bh).
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 TxCCRS:
 III.C. Geometric and Spatial Reasoning – Connections between geometry and other mathematical content strands
 III.C.1. Make connections between geometry and algebraic equations.
 III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
 III.D.1. Find the perimeter and area of twodimensional figures.
 VIII.B. Communication and Representation – Interpretation of mathematical work
 VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.

4.5D 
Solve problems related to perimeter and area of rectangles where dimensions are whole numbers.
Readiness Standard

Solve
PROBLEMS RELATED TO PERIMETER AND AREA OF RECTANGLES WHERE DIMENSIONS ARE WHOLE NUMBERS
Including, but not limited to:
 Rectangle
 4 sides
 4 vertices
 Opposite sides congruent
 2 pairs of parallel sides
 4 pairs of perpendicular sides
 4 right angles
 Square (a special type of rectangle)
 4 sides
 4 vertices
 All sides congruent
 2 pairs of parallel sides
 4 pairs of perpendicular sides
 4 right angles
 Perimeter – a linear measurement of the distance around the outer edge of a figure
 Perimeter is a onedimensional linear measure.
 Whole number side lengths
 Recognition of perimeter embedded in mathematical and realworld problem situations
 Formulas for perimeter from STAAR Grade 4 Mathematics Reference Materials
 Square
 P = 4s, where s represents the side length of the square
 Rectangle
 P = l + w + l + w or P = 2l + 2w, where l represents the length of the rectangle and w represents the width of the rectangle
 Determine perimeter when given side lengths with or without models
 Determine perimeter by measuring to determine side lengths
 Ruler, STAAR Grade 4 Mathematics Reference Materials ruler, yardstick, meter stick, measuring tape, etc.
 Determine missing side length when given perimeter and remaining side length
 Perimeter of composite figures
 Area – the measurement attribute that describes the number of square units a figure or region covers
 Area is a twodimensional square unit measure.
 Whole number side lengths
 Recognition of area embedded in mathematical and realworld problem situations
 Formulas for area from STAAR Grade 4 Mathematics Reference Materials
 Square
 A = s × s, where s represents the side length of the square
 Rectangle
 A = l × w, where l represents the length of the rectangle and w represents the width of the rectangle
 Determine area when given side lengths with and without models
 Determine area by measuring to determine side lengths
 Ruler, STAAR Grade 4 Mathematics Reference Materials ruler, yardstick, meter stick, measuring tape, etc.
 Determine missing side length when given area and remaining side length
 Area of composite figures
 Multiple ways to decompose a composite figure to determine perimeter and/or area
Note(s):
 Grade Level(s):
 Grade 4 introduces solving problems related to perimeter and area of rectangles where dimensions are whole numbers.
 Grade 5 will represent and solve problems related to perimeter and/or area and related to volume.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
 III.D.1. Find the perimeter and area of twodimensional figures.

4.6 
Geometry and measurement. The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties. The student is expected to:


4.6A 
Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines.
Supporting Standard

Identify
PERPENDICULAR AND PARALLEL LINES
Including, but not limited to:
 Line – a set of points that form a straight path that goes in opposite directions without ending
 Parallel lines – lines that lie in the same plane, never intersect, and are always the same distance apart
 Various orientations including vertical, horizontal, diagonal, and parallel lines of even, uneven, or offset lengths
 Notation may be given using chevrons or arrows to represent parallel lines.
 If more than one set of parallel lines are present, the number of chevrons or arrows distinguishes the sets of parallel lines.
 Intersecting lines – lines that meet or cross at a point
 Various orientations including vertical, horizontal, diagonal, and intersecting lines of even, uneven, or offset lengths
 Perpendicular lines – lines that intersect at right angles to each other to form square corners
 Various orientations including vertical, horizontal, diagonal, and perpendicular lines of even, uneven, or offset lengths
 Notation is given as a box in the angle corner to represent a right angle (square corner).
 Lines in polygons
Note(s):
 Grade Level(s):
 Grade 3 used attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and drew examples of quadrilaterals that do not belong to any of these subcategories.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Measuring angles
 Grade Level Connections (reinforces previous learning and/or provides development for future learning)
 TxCCRS:
 III.A. Geometric and Spatial Reasoning – Figures and their properties
 III.A.1. Recognize characteristics and dimensional changes of two and threedimensional figures.

4.8 
Geometry and measurement. The student applies mathematical process standards to select appropriate customary and metric units, strategies, and tools to solve problems involving measurement. The student is expected to:


4.8A 
Identify relative sizes of measurement units within the customary and metric systems.
Supporting Standard

Identify
RELATIVE SIZES OF MEASUREMENT UNITS WITHIN THE CUSTOMARY AND METRIC SYSTEMS
Including, but not limited to:
 Relative size – size in relation to a measure
 Sizes within a single system of measurement (e.g., sizes within customary or sizes within metric systems)
 Typically used units of measure and their relative sizes in words and abbreviations
 Metric unit names are based on prefixes attached to base unit.
 Base units include meter for length, liter for volume and capacity, and gram for mass.
 Kilo: one thousand base units
 Deci: onetenth of a base unit
 Centi: onehundredth of a base unit
 Milli: onethousandth of a base unit
 Length – the measurement attribute that describes a continuous distance from end to end
 Customary units typically used for length
 Inch (in.)
 12 inches (in.) = 1 foot (ft)
 Foot (ft)
 1 foot (ft) = 12 inches (in.)
 3 feet (ft) = 1 yard (yd)
 Yard (yd)
 1 yard (yd) = 3 feet (ft)
 1,760 yards (yd) = 1 mile (mi)
 Mile (mi)
 1 mile (mi) = 1,760 yards (yd)
 Measurement tools typically used for customary length
 Rulers, yardsticks, measuring tapes
 Relative size of customary units of length in realworld context
 Metric units typically used for length
 Millimeter (mm)
 10 millimeters (mm) = 1 centimeter (cm)
 Centimeter (cm)
 1 centimeter (cm) = 10 millimeters (mm)
 100 centimeters (cm) = 1 meter (m)
 Decimeter (dm)
 1 decimeter (dm) = 100 millimeters (mm)
 1 decimeter (dm) = 10 centimeters (cm)
 Meter (m)
 1 meter (m) = 100 centimeters (cm)
 1,000 meters (m) = 1 kilometer (km)
 Kilometer (km)
 1 kilometer (km) = 1,000 meters (m)
 Measurement tools typically used for metric length
 Rulers, meter sticks, measuring tapes
 Relative size of metric units of length in realworld context
 Liquid volume – the measurement attribute that describes the amount of space that a liquid or dry, pourable material takes up, typically measured using standard units of capacity
 Customary units typically used for liquid volume (capacity)
 Fluid ounce (fl oz)
 8 fluid ounces (fl oz) = 1 cup (c)
 Cup (c)
 1 cup (c) = 8 fluid ounces (fl oz)
 2 cups (c) = 1 pint (pt)
 Pint (pt)
 1 pint (pt) = 2 cups (c)
 2 pints (pt) = 1 quart (qt)
 Quart (qt)
 1 quart (qt) = 2 pints (pt)
 4 quarts (qt) = 1 gallon (gal)
 Gallon (gal)
 1 gallon (gal) = 4 quarts (qt)
 Measurement tools typically used for customary liquid volume
 Measuring cups, measuring containers or jars
 Relative size of customary units of liquid volume (capacity) in realworld context
 Metric units typically used for liquid volume (capacity)
 Milliliter (mL)
 1,000 milliliters (mL) = 1 liter (L)
 Liter (L)
 1 liter (L) = 1,000 milliliters (mL)
 1,000 liters (L) = 1 kiloliter (kL)
 Kiloliter (kL)
 1 kiloliter (kL) = 1,000 liters (L)
 Measurement tools typically used for metric liquid volume
 Beakers, graduated cylinders, eye droppers, measuring containers or jars
 Relative size of metric units of liquid volume (capacity) in realworld context
 Weight – the measurement attribute that describes how heavy an object is, determined by the pull of gravity on the object (weight depends upon location)
 Customary units typically used for weight
 Ounce (oz)
 16 ounces (oz) = 1 pound (lb)
 Pound (lb)
 1 pound (lb) = 16 ounces (oz)
 2,000 pounds (lb) = 1 ton (T)
 Ton (T)
 1 ton (T) = 2,000 pounds (lb)
 Measurement tools typically used for weight
 Spring scales, kitchen scales, bathroom scales
 Relative size of customary units of weight in realworld context
 Mass – the measurement attribute that describes the amount of matter in an object (mass remains constant, regardless of location)
 Metric units typically used for mass
 Milligram (mg)
 1,000 milligrams (mg) = 1 gram (g)
 Gram (g)
 1 gram (g) = 1,000 milligrams (mg)
 1,000 grams (g) = 1 kilogram (kg)
 Kilogram (kg)
 1 kilogram (kg) = 1,000 grams (g)
 Measurement tools typically used for mass
 Pan balances, triple beam balances
 Relative size of metric units of mass in realworld context
 Recognition of appropriate unit of measure in realworld context
Note(s):
 Grade Level(s):
 Grade 4 introduces identifying relative sizes of measurement units within the customary and metric systems.
 Grade 5 will solve problems by calculating conversions within a measurement system, customary or metric.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 TxCCRS:
 I.C. Numeric Reasoning – Systems of measurement
 I.C.1. Select or use the appropriate type of method, unit, and tool for the attribute being measured.

4.8B 
Convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.
Supporting Standard

Convert
MEASUREMENTS WITHIN THE SAME MEASUREMENT SYSTEM, CUSTOMARY OR METRIC, FROM A SMALLER UNIT INTO A LARGER UNIT OR A LARGER UNIT INTO A SMALLER UNIT WHEN GIVEN OTHER EQUIVALENT MEASURES REPRESENTED IN A TABLE
Including, but not limited to:
 Whole numbers (0 – 1,000,000,000)
 Products of twodigit factors by twodigit factors and up to fourdigit factors by onedigit factors
 Quotients up to fourdigit dividends by onedigit divisors
 Decimals (less than one or greater than one)
 Limited to multiples of halves (e.g., 0.5, 1.5, 4.5, etc.)
 Determined by reasoning that half of any value is that value divided by 2
 Fractions (proper, improper, and mixed numbers
 Limited to multiples of halves (e.g., etc.)
 Determined by reasoning that half of any value is that value divided by 2
 Onestep conversions from a smaller unit to a larger unit or from a larger unit to a smaller unit
 Conversion – a change from one measurement unit to another measurement unit without changing the amount
 Typically used units of measure
 Customary
 Length: miles, yards, feet, inches
 Volume (liquid volume) and capacity: gallons, quarts, pints, cups, fluid ounces
 Weight: tons, pounds, ounces
 Metric
 Length: kilometer, meter, centimeters, millimeters
 Volume (liquid volume) and capacity: kiloliter, liter, milliliter
 Mass: kilogram, gram, milligram
 Based on prefixes attached to base unit
 Base units include meter for length, liter for volume and capacity, and gram for weight and mass.
 Kilo: one thousand base units
 Deci: onetenth of a base unit
 Centi: onehundredth of a base unit
 Milli: onethousandth of a base unit
 Relationship between converting units
 Converting within the same measurement system, customary or metric
 Multiplication converts larger units to smaller units.
 Division converts smaller units to larger units.
 Convert measurements within the customary measurement system from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.
 Length
 Rule/process column given in a table
 Rule/process column not given in a table
 Volume (liquid volume) and capacity
 Rule/process column given in a table
 Rule/process column not given in a table
 Weight
 Rule/process column given in a table
 Rule/process column not given in a table
 Convert measurements within the metric measurement system from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.
 Length
 Rule/process column given in a table
 Rule/process column not given in a table
 Volume (liquid volume) and capacity
 Rule/process column given in a table
 Rule/process column not given in a table
 Mass
 Rule/process column given in a table
 Rule/process column not given in a table
 Equivalent measures in tables may have missing information in one or both columns.
Note(s):
 Grade Level(s):
 Grade 4 introduces converting measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table.
 Grade 5 will solve problems by calculating conversions within a measurement system, customary or metric.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 I.C. Numeric Reasoning – Systems of measurement
 I.C.2. Convert units within and between systems of measurement.

4.8C 
Solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.
Readiness Standard

Solve
PROBLEMS THAT DEAL WITH MEASUREMENTS OF LENGTH, INTERVALS OF TIME, LIQUID VOLUMES, MASS, AND MONEY USING ADDITION, SUBTRACTION, MULTIPLICATION, OR DIVISION AS APPROPRIATE
Including, but not limited to:
 Whole numbers (0 – 1,000,000,000)
 Products of twodigit factors by twodigit factors and up to fourdigit factors by onedigit factors
 Quotients up to fourdigit dividends by onedigit divisors
 Decimals (greater than one and less than one)
 Addition and subtraction of money amounts up to hundredths
 Conversions limited to multiples of halves (e.g., 0.5, 1.5, 4.5, etc.)
 Determined using reasoning that half of any value is that value divided by 2
 Fractions (proper, improper, and mixed numbers)
 Addition and subtraction of fractions with like denominators
 Conversions limited to multiples of halves (e.g., etc.)
 Determined using reasoning that half of any value is that value divided by 2
 Typically used customary and metric units
 Customary
 Length: miles, yards, feet, inches
 Volume (liquid volume) and capacity: gallons, quarts, pints, cups, fluid ounces
 Weight: tons, pounds, ounces
 Metric
 Length: kilometer, meter, centimeters, millimeters
 Volume (liquid volume) and capacity: kiloliter, liter, milliliter
 Mass: kilogram, gram, milligram
 Based on prefixes attached to base unit
 Base units include meter for length, liter for volume and capacity, and gram for weight and mass.
 Kilo: one thousand base units
 Deci: onetenth of a base unit
 Centi: onehundredth of a base unit
 Milli: onethousandth of a base unit
 Typically used measurement tools
 Customary
 Length: rulers, yardsticks, measuring tapes
 Volume (liquid volume) and capacity: measuring cups, measuring containers or jars
 Metric
 Length: rulers, meter sticks, measuring tapes
 Volume (liquid volume) and capacity: beakers, graduated cylinders, eye droppers, measuring containers or jars
 Mass: pan balances, triple beam balances
 Problem situations that deal with measurements of length
 Addition, subtraction, multiplication, and/or division of measurements of length with or without conversion
 May or may not include using measuring tools to determine length
 Problem situations that deal with intervals of time (clocks: hours, minutes, seconds)
 Addition and subtraction of time intervals in minutes
 Such as a 1 hour and 45minute event minus a 20minute event equals 1 hour 25 minutes
 Time intervals given
 Pictorial models and tools
 Measurement conversion tables
 Analog clock with gears, digital clock, stop watch, number line, etc.
 Time conversions
 1 hour = 60 minutes; 1 minute = 60 seconds
 Fractional values of time limited to multiples of halves
 Elapsed time
 Finding the end time
 Finding the start time
 Finding the duration
 Problem situations that deal with intervals of time (calendar: years, months, weeks, days)
 Time conversions
 1 year = 12 months; 1 year = 52 weeks; 1 week = 7 days; 1 day = 24 hours
 Fractional values of time limited to multiples of halves
 Problem situations that deal with measurements of volume (liquid volume) and capacity
 Addition, subtraction, multiplication, and/or division of measurements of volume (liquid volume) and capacity with or without conversion
 May or may not include using measuring tools to determine volume (liquid volume) and capacity
 Problem situations that deal with measurements of mass
 Addition, subtraction, multiplication, and/or division of measurements of mass with or without conversion
 May or may not include using measuring tools to determine mass
 Problem situations that deal with money
 Addition and subtraction may include whole number or decimal amounts
 Multiplication and division limited to amounts expressed as cents or dollars with no decimal values
 Comparison of money amounts
 Making change
 Range of dollar amounts
Note(s):
 Grade Level(s):
 Grade 3 determined solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15minute event plus a 30minute event equals 45 minutes.
 Grade 4 introduces solving problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.
 Grade 5 will solve problems by calculating conversions within a measurement system, customary or metric.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
 TxCCRS:
 I.A. Numeric Reasoning – Number representations and operations
 I.A.2. Perform computations with rational and irrational numbers.
 III.D. Geometric and Spatial Reasoning – Measurements involving geometry and algebra
 III.D.3. Determine indirect measurements of geometric figures using a variety of methods.
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.3. Determine a solution.
